Deck 5: Trigonometric Functions

Question 1

For evaluate each of the following. Round your answers to four decimal places.

A)

B)

Answer 1

Part A: 0.9951
Part B: 0.9613

Question 2

For evaluate each of the following. Round your answers to four decimal places.

A)

B)

Answer 2

Part A: 0.0149
Part B: 0.7547

Question 3

Given that , find an exact expression for
.

A)

B)

C)

D)

Answer 3

Question 4

Given that , find an exact expression for .

Question 5

Given that , find an exact expression for .

A)

B)

C)

D)

Question 6

Given that , find an exact expression for
.

Question 7

Given that , find an exact expression for .

Question 8

Given that , find an exact expression for .

Question 9

Given that , find an exact expression for .

Question 10

Suppose u is in the interval , with tan(u) = -3. Find an exact expression for tan(-u).

Question 11

Suppose u is in the interval , with tan(u) = -3. Find an exact expression for cos(-u).

A)

B)

C)

D)

Question 12

Suppose u is in the interval , with tan(u) = -9. Find an exact expression for sin(u).

Question 13

Suppose u is in the interval , with tan(u) = -3. Find an exact expression for tan(3 $\pi$ - u).

Question 14

Suppose u is in the interval
, with tan(u) = -2. Find an exact expression for sin(6 $\pi$ + u).

Question 15

Suppose u is in the interval , with tan(u) = -6. Find an exact expression for tan(u - 9 $\pi$ ).

A)

B) 6
C) -6
D)

Question 16

Suppose u is in the interval , with tan(u) = -3. Find an exact expression for .

Question 17

Suppose u is in the interval , with tan(u) = -6. Find an exact expression for .

Question 18

Suppose u is in the interval , with tan(u) = -1. Find an exact expression for .

Question 19

Suppose u is in the interval , with tan(u) = -5. Find an exact expression for sin(8 $\pi$ + u).

A)

B)

C)

D)

Question 20

Suppose u is in the interval , with tan(u) = -3. Find an exact expression for .

Question 21

-Suppose a = 8 and b = 13. Evaluate c. Give the exact answer.

Question 22

-Suppose a = 9 and b = 11. Evaluate sin(u). Give the exact answer.

Question 23

-Suppose a = 7 and b = 8. Evaluate cos(v). Give the exact answer.

Question 24

-Suppose a = 6 and b = 7. Evaluate tan(v).

A)

B)

C)

D)

Question 25

-Suppose b = 6 and c = 7. Evaluate cos(u). Give the exact answer.

Question 26

-Suppose b = 7 and c = 8. Evaluate tan(u). Give the exact answer.

Question 27

-Suppose b = 8 and c = 11. Evaluate sin(v).

A)

B)

C)

D)

Question 28

-Suppose a = 3 and . Evaluate b. Give the exact answer.

Question 29

-Suppose a = 2 and
. Evaluate cos(v). Give the exact answer.

Question 30

-Suppose a = 9 and . Evaluate tan(v).

A)

B)

C)

D)

Question 31

-Suppose c = 8 and u = 1 radian. Evaluate b. Give the exact answer.

Question 32

-Suppose c = 4 and u = 1 radian. Evaluate sin(v). Give the exact answer.

Question 33

-Suppose c = 6 and . Evaluate a. Give the exact answer.

Question 34

-Suppose c = 5 and . Evaluate sin(u).

A)

B)

C)

D)

Question 35

-Suppose c = 17 and
. Evaluate cos(v). Give the exact answer.

Question 36

-Suppose c = 15 and . Evaluate tan(v). Give the exact answer.

Question 37

-Suppose b = 15 and . Evaluate c. Give the exact answer.

Question 38

-Suppose b = 5 and . Evaluate sin(v). Give the exact answer.

Question 39

-Suppose b = 11 and . Evaluate cos(v).

A)

B)

C)

D)

Question 40

Suppose that a 29-foot ladder is leaning against a wall, making a angle with the ground (as measured from a perpendicular line from the base of the ladder to the wall). How many feet up the wall is the end of the ladder, to the nearest tenth of a foot?

Question 41

Find the perimeter of a right triangle that has hypotenuse of length 7 mm and an 18° angle. Round the answer to two decimal places.

Question 42

Find the four smallest positive numbers $\theta$ such that tan(2 $\theta$ ) = 1. Give the exact answers in radians.

Question 43

Suppose and . Evaluate:

A) sin((\theta\))
B) tan( $\theta$ )
Give the exact answers.

Question 44

Suppose and . Evaluate:

A) cos( $\theta$ )
B) tan( $\theta$ )
Give the exact answers.

Question 45

Suppose and . Evaluate:

A) sin( $\theta$ )
B) tan( $\theta$ )
Give the exact answers.

Question 46

Suppose and . Evaluate:

A) cos( $\theta$ )
B) tan( $\theta$ )
Give the exact answers.

Question 47

Suppose and . Evaluate:

A) sin((\theta\))
B) cos( $\theta$ )
Give the exact answers.

Question 48

Suppose and . Evaluate:

A) sin( $\theta$ )
B) cos( $\theta$ )
Give the exact answers.

Question 49

Suppose and . Evaluate:

A) sin( $\theta$ )
B) cos( $\theta$ )
Give the exact answers.

Question 50

Given that , find an exact expression for

A)

B)

C)

D)

Question 51

Given that , find an exact expression for

A)

B)

C)

D)

Question 52

Given that find an exact expression for :

Question 53

Given that , find an exact expression for :

Question 54

Given that , find an exact expression for :

Question 55

Suppose u is in the interval , with tan(u) = 4. Find an exact expression for cot(u).

A) -4
B) 4
C)

D)

Question 56

Suppose u is in the interval , with tan(u) = 9. Find an exact expression for sec(u).

Question 57

Suppose u is in the interval , with tan(u) = 4. Find an exact expression for csc(u).

A)

B)

C)

D)

Question 58

Suppose u is in the interval , with tan(u) = 4. Find an exact expression for sin(u).

Question 59

Suppose u is in the interval , with tan(u) = 3. Find an exact expression for cos(u).

Question 60

Suppose u is in the interval , with cot(u) = 5. Find an exact expression for sec(u).

A)

B)

C)

D)

Question 61

Suppose u is in the interval
, with cot(u) = 9. Find an exact expression for sin(u).

Question 62

Find the equation of the line in the xy-plane that goes through the origin and makes an angle of 0.5 radians with the positive horizontal axis. Round the slope to three decimal places.

Question 63

Find $\theta$ such that tan( $\theta$ ) = for
. Give the exact angle in radians.

Question 64

Give the exact values for the following quantities.
(i) cos(13 $\pi$ ) , (ii) sin(13 $\pi$ )

A) (i) -1, (ii) 1
B) (i) 1, (ii) 0
C) (i) -1, (ii) 0
D) (i) 1, (ii) -1

Question 65

Give the exact values for the following quantities.

A)

B)

Question 66

Give the exact values for the following quantities.

A)

B)

Question 67

Give the exact values for the following quantities.

A)

B)

Question 68

Give the exact values for the following quantities.

A)

B)

Question 69

Give the exact values for the following quantities.
(i) , (ii)

A) (i) , (ii)
B) (i) , (ii)
C) (i) , (ii)
D) (i) , (ii)

Question 70

Give the exact values for the following quantities.

A)

B)

Question 71

Find the smallest number $\theta$ larger than 16 $\theta$ such that cos $\theta$ = 0. Give the exact answer in radians.

Question 72

Find the smallest number $\theta$ larger than 11 $\pi$ such that

A)

B)

C)

D)

Question 73

Find the four smallest positive numbers $\theta$ such that
. Give the exact answers.

Question 74

Find the four smallest positive numbers $\theta$ such that
. Give the exact answers.

Question 75

Find the four smallest positive numbers $\theta$ such that
. Give the exact answers.

Question 76

Find the four smallest positive numbers $\theta$ such that . Give the exact answers.

Question 77

Suppose and . Evaluate sin $\theta$ . Give the exact answer.

Question 78

Suppose And . Evaluate cos $\theta$ .

A)

B)

C)

D)

Question 79

Suppose and . Evaluate sin $\theta$ . Give the exact answer.

Question 80

Suppose and . Evaluate cos $\theta$ . Give the exact answer.